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Noncolliding Brownian motions and Harish-Chandra formula

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1.	Title	Title of document	Noncolliding Brownian motions and Harish-Chandra formula
2.	Creator	Author's name, affiliation, country	Makoto Katori; Chuo university
2.	Creator	Author's name, affiliation, country	Hideki Tanemura; Chiba university
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	random matrices, Dyson's Brownian motion, Imhof's relation, Harish-Chandra formula.
3.	Subject	Subject classification	82B41, 82B26, 82D60, 60G50,
4.	Description	Abstract	We consider a system of noncolliding Brownian motions introduced in our previous paper, in which the noncolliding condition is imposed in a finite time interval $(0,T]$. This is a temporally inhomogeneous diffusion process whose transition probability density depends on a value of $T$, and in the limit $T \to \infty$ it converges to a temporally homogeneous diffusion process called Dyson's model of Brownian motions. It is known that the distribution of particle positions in Dyson's model coincides with that of eigenvalues of a Hermitian matrix-valued process, whose entries are independent Brownian motions. In the present paper we construct such a Hermitian matrix-valued process, whose entries are sums of Brownian motions and Brownian bridges given independently of each other, that its eigenvalues are identically distributed with the particle positions of our temporally inhomogeneous system of noncolliding Brownian motions. As a corollary of this identification we derive the Harish-Chandra formula for an integral over the unitary group.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2003-09-23
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1076
10.	Identifier	Digital Object Identifier	10.1214/ECP.v8-1076
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 8
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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